Steady-State and Stochastic Performance of a Modified Discrete-Time Prototype Repetitive Controller

1990 ◽  
Vol 112 (1) ◽  
pp. 35-41 ◽  
Author(s):  
Kok Kia Chew ◽  
Masayoshi Tomizuka
Keyword(s):  
Steady State ◽  
Discrete Time ◽  
Internal Model ◽  
Repetitive Control ◽  
Signal Generator ◽  
Disk File ◽  
Stochastic Disturbances ◽  
Actuator System ◽  
Dual Objectives ◽  
Steady State Performance

Perfect regulation may be too stringent a condition in repetitive control. In this paper, the rigid stability requirement is relaxed by including an appropriately chosen filter in the repetitive signal generator. Lacking an internal model, perfect regulation is not assured in the modified system. The steady-state and stochastic performances of the resulting system are analyzed. These analyses reveal that under certain conditions the dual objectives of good steady-state and stochastic performances are conflicting. A high repetitive gain may give good steady-state performance, but the variance propagation of stochastic disturbances is large (extremely large for some choice of a parameter in the modified controller). The converse is true when the repetitive gain is small. The performance of the modified scheme is evaluated by applying it to a simulated disk-file actuator system.

Analysis and Synthesis of Discrete-Time Repetitive Controllers

1989 ◽  
Vol 111 (3) ◽  
pp. 353-358 ◽  
Author(s):  
Masayoshi Tomizuka ◽  
Tsu-Chin Tsao ◽  
Kok-Kia Chew
Keyword(s):  
Discrete Time ◽  
Tracking Error ◽  
Disk File ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Analysis And Synthesis ◽  
Holding Device ◽  
Low Pass ◽  
Actuator System ◽  
Repetitive Controller

Repetitive control is formulated and analyzed in the discrete-time domain. Sufficiency conditions for the asymptotic convergence of a class of repetitive controllers are given. The “plug-in” repetitive controller is introduced and applied to track-following in a disk-file actuator system. Inter-sample ripples in the tracking error were present when the “plug-in” repetitive controller was installed. The performance is enhanced, however, when the zero-holding device is followed by a low-pass filter or replaced by a delayed first-order hold.

scholarly journals Discrete-Time Phase Compensated Repetitive Control for Piezoactuators in Scanning Probe Microscopes

2008 ◽  
Author(s):  
Ug˘ur Arıdog˘an ◽  
Yingfeng Shan ◽  
Kam K. Leang
Keyword(s):  
Steady State ◽  
Discrete Time ◽  
Tracking Error ◽  
Repetitive Control ◽  
Scanning Probe ◽  
Two Phase ◽  
Operating Cycle ◽  
Phase Lead ◽  
State Tracking ◽  
Repetitive Controller

This paper studies repetitive control (RC) with linear phase lead compensation to precisely track periodic trajectories in piezo-based scanning probe microscopes (SPMs). Quite often, the lateral scanning motion in SPMs during imaging or fabrication is periodic in time. Because of hysteresis and dynamic effects in the piezoactuator, the tracking error repeats from one scanning period to the next. Commercial SPMs typically employ PID feedback controllers to minimize the tracking error; however, the error repeats from one operating cycle to the next. Furthermore, the residual error can be excessively large, especially at high scan rates. A discrete-time repetitive controller was designed, analyzed, and implemented on an experimental SPM. The design of the RC incorporates two phase lead compensators to provide stability and to minimize the steady-state tracking error. Associated with the lead compensators are two parameters that can be adjusted to control the performance of the repetitive controller. Experimental tracking results are presented that compare the performance of PID, standard RC, and the modified RC with phase lead compensation. The results show that the modified RC reduces the steady-state tracking error to less than 2% at 25 Hz scan rate, an over 80% improvement compared to PID control.

Design and Analysis of Discrete-Time Repetitive Control for Scanning Probe Microscopes

2009 ◽  
Vol 131 (6) ◽  
Author(s):  
Ugur Aridogan ◽  
Yingfeng Shan ◽  
Kam K. Leang
Keyword(s):  
Steady State ◽  
Discrete Time ◽  
Pid Control ◽  
Tracking Error ◽  
Repetitive Control ◽  
Scanning Probe ◽  
Operating Cycle ◽  
Digital Implementation ◽  
Phase Lead ◽  
State Tracking

This paper studies repetitive control (RC) with linear phase lead compensation to precisely track periodic trajectories in piezo-based scanning probe microscopes (SPMs). Quite often, the lateral scanning motion in SPMs during imaging or nanofabrication is periodic. Dynamic and hysteresis effects in the piezoactuator cause significant tracking error. To minimize the tracking error, commercial SPMs commonly use proportional-integral-derivative (PID) feedback controllers; however, the residual error of PID control can be excessively large, especially at high scan rates. In addition, the error repeats from one operating cycle to the next. To account for the periodic tracking error, a discrete-time RC is designed, analyzed, and implemented on an atomic force microscope (AFM). The advantages of RC include straightforward digital implementation and it can be plugged into an existing feedback control loop, such as PID, to enhance performance. The proposed RC incorporates two phase lead compensators to ensure robustness and minimize the steady-state tracking error. Simulation and experimental results from an AFM system compare the performance among (1) PID, (2) standard RC, and (3) the modified RC with phase lead compensation. The results show that the latter reduces the steady-state tracking error to less than 2% at 25 Hz scan rate, an over 80% improvement compared with PID control.

scholarly journals Comparison of Different Repetitive Control Architectures: Synthesis and Comparison. Application to VSI Converters

Electronics ◽  
2018 ◽  
Vol 7 (12) ◽  
pp. 446
Author(s):  
Germán Ramos ◽  
Ramon Costa-Castelló
Keyword(s):  
Internal Model ◽  
Repetitive Control ◽  
Signal Generator ◽  
Experimental Results ◽  
Controller Synthesis ◽  
Voltage Source ◽  
Periodic Signal ◽  
Voltage Source Inverter

Repetitive control is one of the most used control approaches to deal with periodic references/disturbances. It owes its properties to the inclusion of an internal model in the controller that corresponds to a periodic signal generator. However, there exist many different ways to include this internal model. This work presents a description of the different schemes by means of which repetitive control can be implemented. A complete analytic analysis and comparison is performed together with controller synthesis guidance. The voltage source inverter controller experimental results are included to illustrative conceptual developments.

Quasi-steady-state performance of a heat pipe subjected to transient acceleration loadings

10.2514/3.895 ◽  
1997 ◽  
Vol 11 ◽  
pp. 306-309 ◽  
Author(s):  
Edwin H. Olmstead ◽  
Edward S. Taylor ◽  
Meng Wang ◽  
Parviz Moin ◽  
Scott K. Thomas ◽  
...  
Keyword(s):  
Steady State ◽  
Heat Pipe ◽  
Quasi Steady State ◽  
Steady State Performance

A Novel Control Scheme for PWM Boost Converter based on Sliding Mode Control using Particle Swarm Optimization

2020 ◽  
Vol 14 ◽  
Author(s):  
Gang Liu ◽  
Dong Qiu ◽  
Xiuru Wang ◽  
Ke Zhang ◽  
Huafeng Huang ◽  
...  
Keyword(s):  
Particle Swarm Optimization ◽  
Steady State ◽  
Sliding Mode ◽  
Particle Swarm ◽  
Mathematic Model ◽  
Absolute Error ◽  
Boost Converter ◽  
Sliding Mode Controller ◽  
Swarm Optimization ◽  
Steady State Performance

Background: The PWM Boost converter is a strongly nonlinear discrete system, especially when the input voltage or load varies widely, therefore, tuning the control parameters of which is a challenge work. Objective: In order to overcome the issues, particle swarm optimization (PSO) is employed for tuning the parameters of a sliding mode controller of a boost converter. Methods: Based on the analysis of the Boost converter model and its non-linear characteristics, a mathematic model of a boost converter with a sliding mode controller is built firstly. Then, the parameters of the Boost controller are adjusted based on the integrated time and absolute error (ITAE), integral square error (ISE) and integrated absolute error (IAE) indexes by PSO. Results: Simulation verification was performed, and the results show that the controllers tuned by the three indexes all have excellent robust stability. Conclusion: The controllers tuned by ITAE and ISE indexes have excellent steady-state performance, but the overshoot is large during the startup. The controller tuned by IAE index has better startup performance and slightly worse steady-state performance.

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